The Compound Pendulum

1. Introduction
A rigid body with distributed mass able to freely pivot about a horizontal axis 'P' which does not coincide with the centre of gravity is called a compound pendulum.
Let 'G' be the centre of gravity and 'h' the distance of G from the pivot point 'p'.
The moment of inertia of the pendulum about the pivot axis is:

I = M kp2 and from the parallel axis theorem:
I = M( kg2 + h2 ) where kg is the radius of gyration about G

2. Analysis
To determine the periodic time of the pendulum's oscillations use:

Torque = Moment of Inertia x Angular Acceleration

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David J Grieve, 13th November 2001.